Let's talk a little bit about what I find to be one of the
more mysterious forces of the universe.
Actually, I find all of the forces of the universe to be
fairly mysterious, so let's talk a
little bit about charge.
And we've all heard of charge.
Charge the battery.
This particle has charge.
But when you really think about it, all charge means is
that there's this property called charge, and we know
that if something contains a positive charge-- and calling
it positive is a little bit arbitrary.
It's not like protons have a little plus written on them.
We could have called them negative.
But when something has a positive charge and when
something else has a positive charge, that
they repel each other.
We also know that if I had something else, another
particle that happened to have a negative charge, and once
again, the word "negative" being applied to this is
completely arbitrary.
They could have called it blue charge and red charge, but all
we know is that when another object has the other charge--
in this case, we call it negative-- that's going to be
attracted to a positive charge.
So what do we know about charge?
Charge is a property that particles have, and if you put
enough particles together, I guess objects have that
property as well.
So it's just a property.
And that's a way of saying that I really don't
know what it is.
And frankly, no one fundamentally
knows what it is.
Actually, no one really fundamentally knows anything.
But charge is a property of particles and
objects, just like mass.
I mean, if you think about it, mass is just a property.
And to some degree, it seems a little bit more real than
charge, because our brains are wired to in some way
comprehend what mass is, but we're probably comprehending
weight and volume more than mass, but we can think more
about that at another time.
Charge is a little bit more abstract because, before we
started rubbing amber into our hair, we really didn't
experience much charge unless we got struck by lightning.
So charge is a property that particles or objects have, and
we know that there are two types of charge, which we've
arbitrarily named positive and negative.
And we know that like charges repel and opposite charges
attract, or unlike charges attract, right?
So what can we do with this?
Well, if we have this property, I think a useful
thing to do would be to measure the property, and so
we came up with units, and so the unit of charge is called
the coulomb.
It's named after a scientist in the late 1700s, who played
around a lot with charge.
You could look up more about him on Wikipedia.
But it's called the coulomb, and the coulomb-- there's a
bunch of definitions, but I like to think of it in terms
of elementary particles, just because, to some degree,
unless you go into quantum theory and start talking about
quarks and stuff, the elementary charge is the
charge on a proton or a neutron.
So I'll go into more detail in the future on actually the
structure of atoms and whatever else, but let me just
draw a little example.
So an atom tends to have some neutrons in them, which don't
have this charge property.
It'll have some protons in them, which
have a positive charge.
Once again, that's kind of
arbitrarily defined as positive.
We could have called a red charge.
And then it has these things floating around that are much,
much, much lighter than the protons and the neutrons in
the nucleus, and these are called electrons.
It's not even clear that they're real objects.
They're almost like energy, but sometimes it's useful to
view them as objects.
Sometimes it's useful to view them as--
well, not as objects.
And we'll go into all of that more later, but electrons have
a negative charge.
And the fundamental unit of charge, as far as we are
concerned right now before we start talking about quarks and
other potentially subatomic particles, is the charge in an
electron or proton.
And they have the exact same charge, and that elementary
charge is denoted by e.
And to be frank, I'm not sure whether e stands for
elementary or e stands for electron.
But actually, e is equal to the charge of a proton so it
probably stands for elementary charge of a proton.
And the charge of an electron is the negative of this, so
negative e is the charge of an electron.
But if we didn't care about sign, then the
magnitudes are the same.
So that's the fundamental as far as we know or so far in
our physics.
That's the fundamental charge.
The fundamental unit of charge is just the charge in a proton
or neutron.
So how does a coulomb relate to that?
Well, a coulomb, which we'll denote by C, is equal to-- and
this is a bit of an arbitrary number, but when we start
doing things with electricity, we'll see why the coulomb was
defined the way it is, but a coulomb is 6.24 times 10 to
the eighteenth e's.
Or you can say it's 6.24 times 10 to the eighteenth times the
charge on an electron-- actually, times the charge on
a proton, and then, of course, in terms of magnitude.
Because if I just say coulomb, I'm not
really giving a direction.
So if you look at it the other way around, you can say that
the elementary charge is equal to-- at least its magnitude--
1.6 times 10 to the minus 19 coulombs.
So fair enough.
This might be a useful number to memorize, but it will
usually be provided for you in some way.
So what can we do?
We say that these objects have this property called charge.
Like charges repel.
Unlike charges attract.
If we have enough of these protons together, then the
whole object has charge.
If we have more protons than electrons, then we have a
positive charge.
If we have more electrons than protons, we
have a negative charge.
And we know that we've defined this unit of charge called the
coulomb, which is a bunch of the fundamental charge.
So let's play around with this and see if
we can measure charge.
So part of the initial-- I guess we could call it--
definition on what charge is, I said that like charges
repel, right?
Like charges repel so both of these are positive.
They're going to repel each other.
And unlike charges, if this is negative, this is positive,
they're going to attract each other, right?
So by definition, if they are moving each other, these two
particles are going to accelerate
away from each other.
These two particles are going to accelerate
towards each other.
The charge between these particles or the charge in
each of these particles must be generating some type of
force, right?
If there was no force being generated, then they wouldn't
repel or attract each other, and this is where we get to
Coulomb's Law, and this is why we named
charges after Coulomb.
Coulomb figured out that the force between two charges is
equal to-- and this is going to be a vector quantity, and
in about 30 seconds, I'll tell you what happens with the
direction-- is equal to some constant times the first
charge times the second charge divided by the distance
between them squared.
And this is pretty neat because this looks an awful
lot like-- so if we call this the force, the electric force,
that looks a lot like the gravitational force equation.
Let me write that down.
The force from gravity between two masses is equal to the
gravitational constant times m1 times m2 divided by the
distance between them squared.
So far, the two forces that we've covered, gravity, and
now we're covering electric force and we'll eventually
expand this to electromagnetic force, it seems like they kind
of act at distance in a similar way, and both of these
forces apply in a vacuum.
So it doesn't matter if you have no air, if you have no
substances between the two particles, somehow they are
communicating with each other, which I find
kind of amazing, right?
You can have nothing between these two particles, but
somehow, this particle knows that that particle's there and
that particle knows that that particle's there, and they
start moving without having any-- it's not like they have
a wire connected to each other and someone's telling the
other particle, hey, there's a particle there.
Start moving.
So I don't know if you find that as amazing as I do, but
think about it and you might.
And it's just like gravity.
I mean, the two masses are in no way connected.
They could be sitting in a vacuum, but somehow, they know
that the other particle's there.
And when we start learning about special relativity and
all of that, we'll learn that there's nothing there, but
maybe the masses are actually somehow shaping the universe.
And maybe that's happening with the
electric charges as well.
But all we know at this point is that we have these charges
and that they exert a force on each other that's proportional
to the product of their respective charges divided by
the square of the distance between them.
And this constant right here, that is-- I always forget it.
What was it?
I think it's 6.-- I always forget what that constant is.
It is 9 times 10 to the ninth.
It's rounded, of course.
That would be amazing if it was exactly 9.
9 times 10 to the ninth, and the units are newton-meter
squared per coulomb squared.
And why are those the units?
Well, pretty much because at the end, we have coulomb,
coulomb, so we're going to have coulomb squared divided
by meter squared, and we want to finish with newtons, so we
want to cancel out the coulomb squared by putting it in the
denominator.
We want to cancel out the meter squared by putting it in
the numerator, and then we'll end up with the newtons to get
the force, so that's just where the units come from.
So given that, let's figure out the
force between two particles.
So let's say I have-- and I've spent 10 minutes with a pretty
long-winded explanation, but the actual problems you'll see
in your physics class are pretty straightforward when it
comes to Coulomb's Law.
So they'll say, hey, we have a positive-- we have a particle
here that has a positive charge of plus-- let me think
of a good number-- plus 5 times 10 to the minus 3
coulombs, so that's a positive charge.
And then we have a negative charge here, so let's say
that-- I don't know.
How far will I make them?
Let's say that they're half a meter apart, 0.5 meters apart,
and then I have a negative charge here that is 10 minus
10 times 10 to the minus 2 coulombs.
So what is the force between these two particles?
So if we just plug them in to Coulomb's Law, we get the
force due to the electricity.
The electrical force.
Not due to electricity.
We haven't done that yet.
The static electric force between those two particles is
equal to the constant 9 times 10 to the ninth times the
first charge times 5 times 10 to the minus 3 times the
second charge-- let me do that in a different color-- times
minus 10 times 10 to the minus 2-- I just rewrote that,
although you probably can't see it-- divided by the
distance squared, so 0.5 squared.
We just plugged into this formula.
So that equals-- let me see.
So 9 times 0.5 times 10.
I'm just going to do the 10 separately.
So that's times minus 10.
This is 0.5 times minus 10 is minus 5 times 9 is minus 45,
and then 10 to the ninth minus 3, so 10 to the sixth, and
then minus 2, so 10 to the fourth-- times 10 to the
fourth-- divided by-- and what's 0.5 squared?
It's 0.25, right?
And this is equal to what?
That's equal to 4 times this top, 160, plus this is equal
to minus 180 times 10 to the fourth newtons.
And actually, this might seem like a large number, but these
charges that I put here are actually fairly large charges,
and hopefully you'll get a sense for what's a big or a
small charge later.
But these are reasonably large charges, and so that's why
there's a relatively large force exerting between these
two particles.
Now, we got a negative number, so what does that mean?
Well, we know that unlike particles attract, right?
Almost by definition.
In this case, we had a positive and a negative, so
when we end up with a negative force when we use Coulomb's
Law, that means that the force will draw the two particles to
each other along the shortest distance between them.
I mean, it's not going to make them go in a curve.
That kind of makes sense.
If we had a positive there, that means that the force was
repelling the two particles.
And if you ever get confused, just think about it.
If they're both negative, they're going to repel.
If they're both positive, they're going to attract.
I will see you in the next video.